Symmetry Breaking
(Published on 11. October 2024, 16:00 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. For a digit X in a cage with clue Y, the difference X-Y must occur Y cells away along an orthogonal direction.
Background: Symmetry breaking is a concept in theoretical physics with many important consequences. In particular, a distinction is made between “spontaneous” and “explicit” symmetry breaking. This puzzle plays with the latter concept. The rules are symmetric with respect to the spatial directions; the arrangement of the cages is mirror-symmetric with respect to a diagonal; almost all cage clues are also symmetric. Only the small symmetry breaking in a single entry causes the Sudoku as a whole to be uniquely solvable and no longer symmetrical with respect to the diagonal.
The puzzle is in a sense complementary to my puzzle Long-Distance Relationship. There, a digit X in a cage also had to occur X cells away in a diagonal direction; here, the idea is adapted to an orthogonal direction. As digits must not repeat along orthogonal directions, the variant with the specified difference was created instead.
If you are interested in the topic of symmetry, please check out my other Sudokus that are nearly symmetric but employ quite different logic:
Your feedback, ratings and comments are highly appreciated. Have fun!
Solution code: All digits of row 1 (from left to right) followed by column 1 (from top to bottom) without spaces.
